Plateau’s problem for integral currents in locally non-compact metric spaces

Wenger, Stefan

doi:10.1515/acv-2012-0018

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Journal article

Plateau’s problem for integral currents in locally non-compact metric spaces

Wenger, Stefan Department of Mathematics, University of Fribourg, Switzerland

2013

Published in:

Advances in Calculus of Variations. - 2014, vol. 7, no. 2, p. 227–240

English The purpose of this article is to prove existence of mass minimizing integral currents with prescribed possibly non-compact boundary in all dual Banach spaces and furthermore in certain spaces without linear structure, such as injective metric spaces and Hadamard spaces. We furthermore prove a weak*-compactness theorem for integral currents in dual spaces of separable Banach spaces. Our theorems generalize results of Ambrosio–Kirchheim, Lang, the author, and recent results of Ambrosio–Schmidt.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language